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Re: Formula Stirlinga

  • To: mathgroup at smc.vnet.net
  • Subject: [mg130705] Re: Formula Stirlinga
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Sat, 4 May 2013 03:17:41 -0400 (EDT)
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On 5/1/13 at 9:43 PM, karchevskymi at gmail.com wrote:

>n = 1000; N[n! - Sqrt[2*Pi*n]*(n/Exp[1])^n] = 3.35308734163*10^2563
>Why does Stirling's formula works incorrect?

Stirling's formula is a valid approximation. But the way you are
trying to demonstrate that isn't effective. Note

In[1]:= n = 1000;
N[(Sqrt[2*Pi*n]*(n/E)^n)/n!]

Out[2]= 0.999917

In[3]:= 100 (1 - %)

Out[3]= 0.00833299

That is there is an error of about 0.008%

and

In[4]:= Log[10, n!] + Log[10, %/100]

Out[4]= 2563.53

That is an error of 0.008 amounts to a difference of 10^2563




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